Inspired by the"Did Jesus Exist" thread.
Do we have the independant (non muslim) and contemporaneous accounts of Muhammad which we seem to lack for Jesus ?
Yes.
There is a great deal of information available that proves to the satisfaction of most scholars that Muhammad did in fact exist more or less as described.
Care to expand?
Unlike Jesus, Mohammed because a head of state, and quite a formidable one. Don’t think of the historical Mohammed as someone like the historical Jesus - think of him as more akin to Justinian I, of the Byzantine Empire. Justinian’s a saint in the Eastern Orthodox church, with (one assumes) various miracles and other religious properties attributed to him. One can believe in Saint Justinian or not - but Emperor Justinian I was very, very real, and came very close to re-integrating the Western Roman Empire with Byzantium.
So, too, with Mohammed. Was he a prophet? I don’t believe so - as an atheist, I don’t believe anyone was a prophet. But was he a real, historical person who cut quite a swathe through the Middle East in the 600s? Well, someone certainly did a whole bunch of conquering at that time, and the contemporary sources attribute it pretty unanimously to a fellow named Mohammed. (As I understand it). So, the simplest explanation is that the fellow existed.
Actually I’ll need to revise that.
There is a considerable amount of information and evidence available, mostly Arabic writings, some from other sources(Greek, Armenian, Syrian). Not all of the accounts agree; dates are not nearly exact as some would like to think. There is much conflicting information about the man, but what is known for sure is that he was an actual person, most likely some kind of warlord, who may or may not be directly responsible for the creation of Islam.
Right - “head of state” may (or may not) have been too strong a description. The line between warlordism and statesmanship was fuzzier back in the day. 
He killed, therefore he is?
Nitpick: Mohammed conquered/united Arabia only, defining “Arabia” as the Arab peninsula south of Syria/Palestine/Jordan/Iraq. It was his successors who came swarming out of the desert westward and eastward and northward and conquered a vast empire.
So you’re saying Mohamed’s empire was half-vast?
Hey - have you ever conquered Arabia? No? Nor I. I’m willing to call it “vast”. 
He took cities and towns, he cut short limbs and lives.
He made orphans and widows of children and wives.
In this course many years he triumphantly ran,
And did mischief enough to be called a Great Man!
I remember the poem, but I can’t for the life of me remember who wrote it.
I recall seeing a hair of his beard or something in a museum or mosque type place in Turkey. Could THAT have been his real hair? My memory is pretty bad though so it might have been another famous Muslim’s beard hair.
Ask any Muslim and he will tell you that Mohammed did not create Islam. This is a myth.
Muslims practiced Islam way before Mohammed. Jesus practiced Islam. Jesus was a Muslim, Jews are Muslims technically. Unfortunately the word has been twisted to mean today’s modern Muslims but that is not correct.
Islam is purely laillahilallah.
(There is no God but Allah) meaning there is only one God. The same God of Jews and Christians. The people of the books. Monotheists. Followers of the Abrahamic religion.
That is why today’s Muslims believe in Jesus and all the other prophets. Jesus is in the Quran.
They are all Muslims.
Their followers today however they don’t believe are Muslim, true Muslim that is because they now worship the prophet Jesus and not God himself. That’s the difference and that’s where Jews and Muslims are similar. They do not believe Jesus was or is God.
Other religions have similar beliefs, and Islam certainly has a lot in common with the other Abrahamic religions. But if you ask a historian they won’t agree with you.
No, it is not. It is a non-religious statement. The rest of your comment is a … theological conceit.
We are talking about a word here ‘Islam’.
It’s not important what historians believe, it’s important to translate the word correctly and it’s meaning by Arabs whose language it is.
So Islam is the practice of following ‘one God’ one Allah.
illaha means the word god/deity.
Allah is God’s actual name. Allah does not mean deity as some people think.
Therefore
la (no) illaha (deity) illallah (but God)
So anyone if you are talking in Arabic who believes in ‘one God’ is following Islam. A belief in only one god, and that god is the god of the Abrahamic faiths name is Allah in Arabic.
Jews and Christians therefore follow Islam. A belief in one god.
are you an Arab or Arabic speaker?
What does Islam mean in Arabic then?
I guess not
Islam comes from the root SLM
This means to submit.
In the context we are discussing now which is religion and I am talking specifically the Quran. Islam from the root SLM means to submit to ‘one God’. The various forms of SLM found in the Quran are discussing submission to God and his will. Ask any native Arabic speaking Muslim. there are not too many though around the world granted.
edit add
there are not too many though around the world granted. Outside the Middle East and the Maghreb region.
We’re discussing whether or not Muhammad existed, so yes, what historians believe is important. They’re the ones who look at stories like these and find out what they’re based on. So I disagree with you, and you’re going to get people on this site to agree with you on this point. Muslims believe all people of the book are Muslims. Fine. Historically, the religion was founded by Muhammad about 1400 years ago. Not that I’m a historian but I’ve never heard anyone suggest Muhammad didn’t exist.
We know. That’s the first thing you hear about Islam in any school textbook, and most of us probably heard it in high school.